Addendum: Gravitational memory: new results from post-Newtonian and self-force theory (2025 Class. Quantum Grav. 42 135009)

In Cunningham et al (2025 Class. Quantum Grav.42 135009), we made use of the recent completion of the oscillatory piece of the waveform at third-and-a-half post-Newtonian (3.5PN) order (Henry 2023 Phys. Rev. D107 044057) to obtain the GW memory piece for non-spinning binary black holes. However, the latter reference also contains the spinning contributions to the oscillatory waveform for non-precessing systems. In this Addendum, we take advantage of this fact to compute the non-oscillatory, memory piece at 3.5PN for non-precessing, spinning binary black holes. This completes the 3.5PN waveform, including both oscillatory and memory effects in the non-spinning and spinning sectors. Crucially, this computation required controlling the spin-induced absorption effects due to the black-hole horizons. Our result is fully consistent with the results at 5PN and leading order in the mass ratio obtained in our main paper using analytical self-force techniques for a non-spinning particle around a Kerr black hole (a ≠ 0). We also take advantage of this computation to present in one place a certain number of important quantities (energy, energy flux at infinity, horizon energy flux, and phasing) in the case of spinning, non-precessing, binary black hole systems on circular orbits, at 3.5PN and to all orders in spin. These results were for the most part known, but were scattered throughout the literature. Finally, we include in this Addendum an ancillary file, which contains most lengthy results in machine-readable form.